What's confirmed
Aniipod Ultra and the Sparkling Cube both guarantee a successful catch, no roll involved source
The Tumbler multiplies catch chance ×2 normally, ×6 specifically during a Wild Surge source
Landing a Break raises catch chance ×1.5, up to ×3 with the Break catch-bonus perk active source
Base catch chance is set per zone and catch-difficulty tier: 56/42/28% in Standard Areas, falling to 32/24/16% by the Late Stage source
A throw is decided by two independent rolls, each at the square root of the Final Chance; both must succeed, and a Final Chance of 100% or higher is a guaranteed catch source
More systems: Aniimo Exchange, Boss Rush, Branches & Lumin Amber, Aniimo Consignment, Egg Heist, Eggs & Hatching, Held Items & Contracts, Holo-Battle Sim, Homeland, Legendary Capture & the Legendary Aniipod, Prismana Flow & Nurture, Home Recipes, Regional Forms (Morphology), Resonance, Rift Catcher, Unlocking Skills, Sparkling Aniimo, Tutorials, Twining, Umbral Aniimo, Weather & Weather Spawns, Alpha & Omega World Bosses